EE 126. Probability and Random Processes
Current Schedule (Fall 2013)
Catalog Description: (4 units) Three hours of lecture and one hour of discussion per week. This course covers the fundamentals of probability and random processes useful in fields such as networks, communication, signal processing, and control. Sample space, events, probability law. Conditional probability. Independence. Random variables. Distribution, density functions. Random vectors. Law of large numbers. Central limit theorem. Estimation and detection. Markov chains.
Prerequisites: EE 20n. (Math 54 strongly recommended)
Course objectives: This course introduces probability and probalistic models. The objective is to equip students with the basic tools required to build and analyze such models in both the discrete and continuous context. The ideas of bounding and time-dependence are introduced as well.
- Basic probability: sample spaces, events, and probability functions. Independence and conditioning on events using Bayes rule.
- Discrete random variables: Uniform, Bernoulli, Geometric, probability mass functions, conditioning on random variables. Counting arguments.
- Summary statistics: Expectations, variances, moment generating functions
- Continuous random variables: Uniform, Exponential, Gaussian, probability density functions, jointly continuous random variables, conditioning on continuous or discrete random variables.
- Laws of large numbers and bounding: Markov Inequality, Chebychev Inequality, Chernoff Bounding, Weak law of large numbers, Central Limit Theorem
- Estimation: Very basic MMSE and LLSE estimation
- Stochastic Processes: Bernoulli processes and basic Poisson processes. Finite state Markov chains, stationary distributions, and recurrent classes.